{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 损失函数、代价函数与目标函数  \n",
    "  损失函数（Loss Function）：是定义在单个样本上的，是指一个样本的误差。  \n",
    "  代价函数（Cost Function）：是定义在整个训练集上的，是所有样本误差的平均，也就是所有损失函数值的平均。  \n",
    "  目标函数（Object Function）：是指最终需要优化的函数，一般来说是经验风险+结构风险，也就是（代价函数+正则化项）。  \n",
    "  \n",
    "- 几种常见的损失函数  https://www.cnblogs.com/lliuye/p/9549881.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 激活函数\n",
    "\n",
    "机器学习中常用激活函数和损失函数\n",
    "- https://www.cnblogs.com/xiaobingqianrui/p/11346382.html#_label1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.misc import derivative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    y = 1 / (1 + np.exp(-x))\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tanh(x):\n",
    "    return (np.exp(x) - np.exp(-x)) / (np.exp(x)+np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def relu(x):\n",
    "    return [max(xi,0) for xi in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def elu(x,a=1):\n",
    "    y = []\n",
    "    for xi in x:\n",
    "        if xi >= 0:\n",
    "            y.append(xi)\n",
    "        else:\n",
    "            y.append(a*(np.exp(xi)-1))\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softplus(x):\n",
    "    return np.log(1+np.exp(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def derivative_f(func,input,dx=1e-6):\n",
    "    y = [derivative(func,x,dx) for x in input]\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5,5,1000)\n",
    "\n",
    "flg = plt.figure(figsize=(15,5))\n",
    "ax1 = flg.add_subplot(1,2,1)\n",
    "ax1.axis([-5,5,-2,2])\n",
    "plt.xlabel(r'active function',fontsize=18)\n",
    "ax1.plot(x,sigmoid(x),'r-',label='sigmoid')\n",
    "ax1.plot(x,tanh(x),'g--',label='tanh')\n",
    "ax1.plot(x,relu(x),'b-',lw=1,label='relu')\n",
    "ax1.plot(x,softplus(x),'y--',label='softplus')\n",
    "ax1.plot(x,elu(x),'b--',label='elu')\n",
    "ax1.legend()\n",
    "ax2 = flg.add_subplot(1,2,2)\n",
    "plt.xlabel(r'derivative',fontsize=18)\n",
    "ax2.plot(x,derivative_f(sigmoid,x),'r-',label='sigmoid')\n",
    "ax2.plot(x,derivative_f(tanh,x),'g--',label='tanh')\n",
    "ax2.plot(x,derivative_f(softplus,x),'y-',label='softplus')\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 损失函数、代价函数与目标函数  \n",
    "  损失函数（Loss Function）：是定义在单个样本上的，是指一个样本的误差。  \n",
    "  代价函数（Cost Function）：是定义在整个训练集上的，是所有样本误差的平均，也就是所有损失函数值的平均。  \n",
    "  目标函数（Object Function）：是指最终需要优化的函数，一般来说是经验风险+结构风险，也就是（代价函数+正则化项）。  \n",
    "  \n",
    "- 几种常见的损失函数  https://www.cnblogs.com/lliuye/p/9549881.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### （4）对数损失函数（logarithmic loss function）\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$L(y,p(y|x))=−logp(y|x)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "- 该损失函数用到了极大似然估计的思想。P(Y|X)通俗的解释就是：在当前模型的基础上，对于样本X，其预测值为Y，也就是预测正确的概率。由于概率之间的同时满足需要使用乘法，为了将其转化为加法，我们将其取对数。最后由于是损失函数，所以预测正确的概率越高，其损失值应该是越小，因此再加个负号取个反。\n",
    "- 根据上面的内容，逻辑回归中采用的是对数损失函数。将下面两式进行合并可以写成最后的交叉熵损失函数$L(\\theta(x))$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$P(y=1|x,\\theta ) = h_{\\theta}(x)\\\\\n",
    "P(y=0|x,\\theta ) = 1-h_{\\theta}(x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$L(\\theta(x)) = -\\sum_{i=1}^Ny_i * \\log\\theta(x_i)+(1-y_i)\\log(1-\\theta(x_i))$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 交叉熵损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$H(p,q) = - \\sum_{i=1}^{N} p(x^{(i)}) \\log {q(x^{(i)})}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "交叉熵是用来评估当前训练得到的概率分布与真实分布的差异情况，减少交叉熵损失就是在提高模型的预测准确率。其中 p(x) 是指真实分布的概率， q(x) 是模型通过数据计算出来的概率估计。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "二分类模型的交叉熵损失函数就是上面逻辑回归的损失函数$L(\\theta(x))$  \n",
    "那么其代价函数为："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$L(w,b) = -\\frac{1}{N} \\sum_{i=1}^{N} (y^{(i)} \\log {f(x^{(i)})} + ( 1- y^{(i)}) \\log {(1- f(x^{(i)})}))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中 f(x) 可以是sigmoid函数。或深度学习中的其它激活函数。而 y(i)∈0,1 。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## softmax  \n",
    "在二分类任务中，输出层使用的激活函数为 sigmoid   可以想象神经网络分配一个神经元就可以了  \n",
    "而对于多分类的情况，就需要用到softmax 激活函数给每个类都分配一个概率。  神经网络分配多个神经元（2分类的话2个）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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